Interesting all. We may have to rejoin this discussion after the final episode next week. By the content of the thread though, we may have to do it in Cafe Society…
You think so? I see it the other way. Our experimenting with electromagnetism gave us Maxwell’s equations, which, when manipulated mathematically, give us the idea that the speed of light is constant. Add this to the Michelson-Morley experiment and everyone knew that something was way wrong with our Newtonian understanding. Einstein just had the gumption to do the math and derive what the relativistic world must be like, given that the speed of light is constant.
Using advanced math to manipulate what experiment shows us is still empiricism in my book.
KoalaBear: Intuitivism? Have you tried pronouncing your interesting neologism?
Even if Einstein’s breakthroughs were based on thought experiments, I don’t think that Darwin falls in the same category. IANA evolutionary biologist, but I don’t believe Darwin’s work was particularly “intuitivistic.” He saw examples of species that had mutated from island to island in the Galapagos. Fairly empirical.
I can prove that “good” is not the same as “evil.” They’re spelled differently.
These science shows often have the problem of deciding what pictures to use while trying to explain some difficult concept. They don’t want to use talking heads the whole hour, and trying to show the math won’t work, either. So you have to find or make something that represents the concept while the narration explains it. It’s difficult, and there’s always the risk that pretty pictures will distract from, instead of explain, the “text.” But I think The Elegant Universe did a pretty good job of using sophisticated computer graphics and effects to illustrate complex concepts.
What people who make these shows usually say is that they can’t teach anyone all about string theory (or relativity or QM) in an hour, but they can inspire people to seek out more information from books and other sources. And for those who don’t bother to do that, at least they get a passing acquaintance with the concepts.
The program was two hours.
Gravity is an observable property of mass, so I think it would have been discovered eventually whether Newton came along to enlighten us or not. But I’m not sure time dilation (for example) is something that would necessarily reveal itself to anybody who bothered to check the math.
Relativity as a theory is greater than the sum of its equations, which is why its predictions are still being tested today. Einstein insisted that reality would behave precisely the way he imagined it, and so far he’s never been contradicted by experiment. That’s pretty amazing when you consider he had no a priori knowledge of a Relativistic universe upon which to base his assumptions.
Lick your lips and repeat after me: \Intu"itiv*ism. You may want to sound the syllables out before attempting the whole word at once.
The word might be misappropriated in this context, but it’s not a neologism. It refers to the human capacity to recognize truth in the absence of objective criteria or even a linear chain of reasoning – e.g., “I cannot define obscenity, but I know it when I see it.” (I tend to think intuition is the mechanism by which nature evades the limitation incompleteness would otherwise impose on the human intellect, but that’s a discussion for another thread.)
But how could he know that mutation was the answer in advance of the question of evolution? The Origin of Species was published years before Mendel’s Experiments in Plant Hybridization, and the mechanism of heredity itself wasn’t known until the 1950s. IA also NA evolutionary biologist, but it seems to me that natural selection would have been a bit of a stretch in a world in which evolutionary biology did not yet exist.
Alternatively, consider Copernicus and his heretical supposition of a heliocentric universe. From the perspective of an observer on Earth, the sun behaves exactly the same way whether it revolves around us, or us around it – it was pure intuition on Copernicus’ part to “know” which of those models was the correct one given that any empirical evidence that would support his beliefs (such as a reliable calendar) was the outcome of his achievement and not the precipitator thereof.
Now, with respect to string theory I’m open to the possibility it may be true even if it isn’t as yet verifiable because the greatest advancements in science all seem to relate to someone’s ability to “smell” the underlying reality. But I’m haunted by the words of the scientist interviewed on The Elegant Universe who said, “if a theory doesn’t produce a testable hypothesis, then nobody should believe it.”
This is not a major disagreement, KoalaBear, I just think that that Einstein’s development of relativity was a true thought experiment, and Darwin’s work was not. Darwin had the physical evidence in front of him, which led him to ponder mechanisms by which the differentiations could come about. Throughout that whole process, he collected and considered physical evidence that would support or falsify his theories.
Einstein asked “what would happen if I rode on a beam of light,” and logicially (and mathematically) considered the ramifications of that and other possibilities. Aside from the known failure of the Michelson-Morley experiments (to detect the ether) he relied very little on experimental observations or previous scientific research.
Also not exactly the same, since the helocentric theory would be preferred by applying Occam’s Razor. IIRC (and it’s been 20 years since I read Copernicus, but I could look this up if you like), Copernicus was troubled by the speed that would required of the stars to spin around the earth once a day, and thought it much more likely that the Earth rotated on its axis. Once you grant that, the Earth moving around the sun is the more obvious reason for the sun’s apparent motion through the stars.
The two world systems were mathematically equivalent, but, as you suggest, the geocentric view was based primarily on the dogmatic view that God created the Earth (and hence Man) at the center of the universe. The heliocentric view greatly simplified the mechanisms needed to explain the appearances of the motions of the planets and the sun. However, we should note that because Copernicus himself was dogmatically stuck on the “need” for circular orbits, his heliocentric view was not in fact simpler, and also used the epicycles, eccentrics, etc. of the Ptolomaic world view. It took Kepler, almost a century later, to posit elliptical orbits, and thus the simplest (in fact, the true) heliocentric system.
I’d say that all these cases illustrate an ability to reject the social and scientific conventions of the day and consider all options, regardless of how unusual they may seem at first.
I suspect the scientist (Sheldon Glasow, IIRC) didn’t use the word "believe, but probably said “accept.” In my opinion, “true but not verifiable” is a contradiction in terms. String theory has a certain elegance that has often accompanied hypotheses that were later proved to be true, but if in fact no experiment or observation can ever prove or falsify ST, then it can only be a nice story, not scientific fact, and therefore not true in any meangful sense of that word. Feel free to believe in string theory. Just don’t assert that it’s true.
They said on the show that there is a contradiction between Quantum Mechanics and General Relativity - that they both can’t be correct. They are hoping that string theory will resolve the problem.
Can someone here explain what the contradiction is?
This is at least partly due to the fact that string theory is a much broader theory. String theory, if it works, promises to unify (and thus completely explain) all of the forces of nature. This appeals to anyone working with any of the forces at a fundamental level, escpecially since our understanding of the Strong Force is still so painfully incomplete (currently, we can only understand the Strong Force properly in high-energy (small scale, high frequency) interactions). On the other hand, loop quantum gravity is only applicable to gravity. An understanding of loop quantum gravity would probably not give us any significant insight into the Strong Force or other forces. Both models seem to have about the same amount of objective support, and both are about the same difficulty, but string theory offers potentially much higher payoffs, so it gets more attention.
And KoalaBear, Einstein absolutely did not insist anything. He made some guesses, and it’s a mark of his genius that his guesses were so right. But he was the first to aknowledge that even a single experiment contrary to his predictions would prove him wrong. Intuitition and mathematics are wonderful things, but experiment always trumps intuition.
There are several conradictions, the only one I remeber though is that time and spatial dimensions are in different orders in the time-dependent Schroedinger equation (that is to say that the the spatial dimensions appear as psi del-squared whereas the time appears as the partial differential of psi with respect to time), this is obviously not compatible with the idea of space-time which is vital to genral relativity.
The Planck energy (sqrt(h c^5/G)) is about 10^28 eV. Currently accelerators can reach about one TeV (10^12 eV). To reach the Planck length, we would need an accelerator a thousand trillion times more powerful than we have now.
The stringy predictions of effects on gravity at measureable lengths have now been disproved, as Chronos pointed out. Does this disprove string theory? Of course not, according to the string theorists. Those predictions were never really any good, they say. Thus, this “prediction” of string theory goes the way of many others over the past 25 years (e.g. large-mass “relic” particles) that have been disproven.
So, I repeat: string theory has never made a successful prediction. It has made many unsuccessful predictions, which somehow seem to be forgotten by the string theorists as soon as they are ruled out experimentally.
That’s a bit unfair. Despite the name, “string theory” is not one theory, but a whole class of different models. Some versions of string theory did, in fact, predict millimeter-scale effects on gravity, but not all of them. If we had detected those millimeter-scale effects, then that would have been a strong validation of those versions of string theory, and a big step forward in our understanding. As it is, since those tests came up null, those particular versions of string theory are conclusively disproven. But this does not disprove the other forms of string theory. It is admittedly very worrisome that string theories have never made a verified prediction not made by other theories. But neither have any results been found which directly contradict string theory.
As for unifying relativity and quantum mechanics, the core of the problem is not the Schrodinger equation. The idea of spacetime is fundamental not just to General Relativity (which describes gravity), but also to Special Relativity, and quantum mechanics can be (and has been) brought into line with SR. You need to use the Dirac Equation rather than the Schrodinger Equation, but it works.
The real core of the problem is that gravity is not renormalizable. In any quantum field theory, you end up with predictions for physical quantities that are infinite, which is clearly not physical. In theories like QED (quantum electrodynamics, the quantum explanation of the electromagnetic force) you can use a trick called renormalization, which basically lets you cancel out infinities with negative infinities of the “same size” (the actual procedure is a lot more mathematically rigorous than this, of course). But for reasons I’ll not get into, you can’t do this with gravity, which means that you’re inescapably stuck with any infinities you stumble across.
Nitpick: gravity is not perturbatively renormalizable. Although it’s not my field, I’m not aware of any proof that gravity is not renormalizable in general.